I've actually been thinking about Ulrich's future the last couple of days, and how 5e handles apprentice training. Or doesn't, as the case may be.
Technically, Ulrich is Tria ex Bonisagus's apprentice, and is being fostered to Apollodorus. But I would have no problem with him being Laetitia's apprentice. (In fact, I think he would love it, what with his combination of Venus's Blessing and Lecherousness, and her combination of high Presence and Venus's Blessing.) He currently has six Virtues and Flaws, so he has four slots available in addition to his free Puissant Intrigue that he would get as a political Bonisagus (as is his dominae).
His original character sheet (when he was Silviatos's apprentice) had the Virtues Inoffensive to Animals, Study Bonus, and Diedne Magic, and the Flaws Dark Secret (Diedne Lineage), Deleterious Circumstances (in cities), and Twilight Prone, in addition to the V/F that he currently has now. The set that he had when I made him fit the character concept that I originally had as Silviatos's apprentice, since they reflected his former master and what I understood of his Lineage to some degree.
Things have changed, however, and I'm not sure that I would choose the same set of Virtues and Flaws for Ulrich the future Bonisagus as I had for Ulrich the future Ex Misc.
All that being said, how does a character get new virtues and flaws in apprenticeship? I'm assuming that he will still need to be balanced vis-a-vis Virtues and Flaws at gauntlet. I have a vague long-term vision (of him becoming a Bonisagus Trianomae, at least as much as anyone with Sheltered Upbringing can be...that is, no Winston Churchill, but no Neville Chamberlain either).
I'm also pretty open-minded with whatever he's taught be whomever, or whatever assignments or work he may be given...as long as it's not wiping anybody's catatonic mother's bum. After all, he is a "mere" apprentice. Since he's being fostered by/to Apollodorus, though, I would assume that he would have the final say on what Ulrich does or does not.
Also, he was apprenticed in 1217, as near as I can recall, so he has about eleven more years in his apprenticeship.